In order to increase levels of device integration for integrated circuit and other semiconductor devices, there is a drive to produce device features having smaller and smaller dimensions. In today's rapidly advancing semiconductor manufacturing industry, there is a related drive to produce such device features in a reliable and repeatable manner.
Optical lithography systems are commonly used in the fabrication process to form images of device patterns upon semiconductor substrates. The resolving power of such systems is proportional to the exposure wavelength; therefore, it is advantageous to use exposure wavelengths that are as short as possible. For sub-micron lithography, deep ultraviolet light having a wavelength of 248 nanometers or shorter is commonly used. Wavelengths of interest include 193 and 157 nanometers.
At ultraviolet or deep ultraviolet wavelengths, the materials used to form the lenses, windows, and other optical elements of the lithography system, are of critical significance. Such optical elements must be compatible with the short wavelength light used in these lithography systems.
Calcium fluoride and other cubic crystalline materials such as barium fluoride, lithium fluoride, and strontium fluoride, represent some of the materials being developed is for use as optical elements for 157 nanometer lithography, for example. These single crystal fluoride materials have a desirably high transmittance compared to ordinary optical glass and can be produced with good homogeneity.
Accordingly, such cubic crystalline materials are useful as optical elements in short wavelength optical systems such as wafer steppers and other projection printers used to produce small features on substrates such as semiconductor and other wafers used in the semiconductor manufacturing industry. In particular, calcium fluoride finds particular advantage in that it is an easily obtained cubic crystalline material and large high purity single crystals can be grown.
A primary concern for the use of cubic crystalline materials for optical elements in deep ultraviolet lithography systems is anisotropy of refractive index inherent in cubic crystalline materials; this is referred to as “intrinsic birefringence.” It has been recently reported [J. Burnett, Z. H. Levine, and E. Shipley, “Intrinsic Birefringence in 157 nm materials,” Proc. 2nd Intl. Symp on 157 nm Lithography, Austin, Intl SEMATEC, ed. R. Harbison, 2001] that cubic crystalline materials such as calcium fluoride, exhibit intrinsic birefringence that scales as the inverse of the square of the wavelength of light used in the optical system. The magnitude of this birefringence becomes especially significant when the optical wavelength is decreased below 250 nanometers and particularly as it approaches 100 nanometers. Of particular interest is the effect of intrinsic birefringence at the wavelength of 157 nanometers (nm), the wavelength of light produced by an F2 excimer laser favored in the semiconductor manufacturing industry.
Birefringence, or double-refraction, is a property of refractive materials in which the index of refraction is anisotropic. For light propagating through a birefringent material, the refractive index varies as a function of polarization and orientation of the material with respect to the propagation direction. Unpolarized light propagating through a birefringent material will generally separate into two beams with orthogonal polarization states.
When light passes through a unit length of a birefringent material, the difference in refractive index for the two ray paths will result in an optical path difference or retardance. Birefringence is a unitless quantity, although it is common practice in the lithography community to express it in units of nm/cm. Birefringence is a material property, while retardance is an optical delay between polarization states. The retardance for a given ray through an optical system may be expressed in nm, or it may be expressed in terms of number of waves of a particular wavelength.
In uniaxial crystals, such as magnesium fluoride or crystal quartz, the direction through the birefringent material in which the two refracted beams travel with the same velocity is referred to as the birefringence axis. The term optic axis is commonly used interchangeably with birefringence axis when dealing with single crystals. In systems of lens elements, the term optical axis usually refers to the symmetry axis of the lens system. To avoid confusion, the term optical axis will be used hereinafter only to refer to the symmetry axis in a lens system. For directions through the material other than the birefringence axis, the two refracted beams will travel with different velocities. For a given incident ray upon a birefringent medium, the two refracted rays are commonly described as the ordinary and extraordinary rays. The ordinary ray is polarized perpendicular to the birefringence axis and refracts according to Snell's Law, and the extraordinary ray is polarized perpendicular to the ordinary ray and refracts at an angle that depends on the direction of the birefringence axis relative to the incident ray and the amount of birefringence. In uniaxial crystals, the birefringence axis is oriented along a single direction, and the magnitude of the birefringence is constant throughout the material. Uniaxial crystals are commonly used for optical components such as retardation plates and polarizers.
In contrast, however, cubic crystals have been shown to have both a birefringence axis orientation and magnitude that vary depending on the propagation direction of the light with respect to the orientation of the crystal lattice. In addition to birefringence, which is the difference in the index of refraction seen by the two eigenpolarizations, the average index of refraction also varies as a function of angle of incidence, which produces polarization independent phase errors.
Crystal axis directions and planes are described herein using Miller indices, which are integers with no common factors and that are inversely proportional to the intercepts of the crystal planes along the crystal axes. Lattice planes are given by the Miller indices in parentheses, e.g. (100), and axis directions in the direct lattice are given in square brackets, e.g. [111]. The crystal lattice direction, e.g. [111], may also be referred to as the [111] crystal axis of the material or optical element. The (100), (010), and (001) planes are equivalent in a cubic crystal and are collectively referred to as the {100} planes. For example, light propagating through an exemplary cubic crystalline optical element along the [110] crystal axis experiences the maximum birefringence, while light propagating along the [100] crystal axis experiences no birefringence.
Thus, as a wavefront propagates through an optical element constructed from a cubic crystalline material, the wavefront may be retarded because of the intrinsic birefringence of the optical element. The retardance magnitude and orientation may each vary, because the local propagation angle through the material varies across the wavefront. Such variations may be referred to as “retardance aberrations.” Retardance aberrations split a uniformly polarized wavefront into two wavefronts with orthogonal polarizations. Each of the orthogonal wavefronts will experience a different refractive index, resulting in different wavefront aberrations. These aberrations are capable of significantly degrading image resolution and introducing distortion of the image field at the wavelengths of interest, such as 157 nm, particularly for sub-micron projection lithography in semiconductor manufacturing. It can be therefore seen that there is a need in the art to compensate for wavefront aberrations caused by intrinsic birefringence of cubic crystalline optical elements, which can cause degradation of image resolution and image field distortion, particularly in projection lithography systems using light having wavelengths in the deep ultraviolet range.